Numerical simulation of a spin glass

P. Dayal

I. Morgenstern

Barbara Coluzzi B, Preprint Roma N

We study the 4d Heisenberg spin glass model with Gaussian nearestneighbor interactions. We use finite size scaling to analyze the data. We find a behavior consistent with a finite temperature spin glass transition. Our estimates for the critical exponents agree with the results from "-expansion. PACS Numbers 7510N-0270 Preprint Roma1 n o 1054 The lower critical dimension d l of the short range models remains one of the most controversial questions in the spin glass [1]-[3] theory. In the last ten years a consistent number of works has been devoted to studying the Ising model, which seems to be [4, 5] very close to d l in d = 3. In the case of the short range isotropic Heisenberg spin glass, the conclusions of various computer simulations in d = 3 [6, 7] agree that the system is below d l . Using domain wall renormalization group techniques, it was argued [2, 3] that d l = 4 for this model. To our knowledge, there are no previous numerical simulations on the 4d Heisenberg spin glass...

Giorgio Parisi A, Juan Jesus Ruiz-Lorenzo, Daniel A. Stariolo

By means of extensive computer simulations we analyse in detail the two-dimensional Ising spin glass with ferromagnetic next-nearest-neighbour interactions. We found a crossover from ferromagnetic to `spin glass'-like order both from numerical simulations and analytical arguments. We also present proof of a second crossover from the `spin glass' behaviour to a paramagnetic phase for the largest volume studied.

Koji Fukushima, 福島 孝治

Sergio Perez-Gaviro, Juan Jesus Ruiz-Lorenzo, Alfonso Tarancón

Using the decay of the out equilibrium spin-spin correlation function we compute the equilibrium Edward-Anderson order parameter in the three dimensional binary Ising spin glass in the spin glass phase. We have checked that the Edward-Anderson order parameter computed from out of equilibrium numerical simulations follows with good precision the critical law as determined in experiments and in numerical studies at equilibrium. We have also studied the dependence of the order parameter with the lattice size. Finally we present a large time study of the scaling of the off-equilibrium fluctuation-dissipation relations.